# ?lanhs

Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

## Syntax

val = slanhs( norm, n, a, lda, work )

val = dlanhs( norm, n, a, lda, work )

val = clanhs( norm, n, a, lda, work )

val = zlanhs( norm, n, a, lda, work )

## Include Files

• Fortran: mkl.fi
• C: mkl.h

## Description

The function ?lanhs returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A.

The value val returned by the function is:

val = max(abs(Aij)), if norm = 'M' or 'm'

= norm1(A), if norm = '1' or 'O' or 'o'

= normI(A), if norm = 'I' or 'i'

= normF(A), if norm = 'F', 'f', 'E' or 'e'

where norm1 denotes the 1-norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(Aij)) is not a consistent matrix norm.

## Input Parameters

norm

CHARACTER*1. Specifies the value to be returned by the routine as described above.

n

INTEGER. The order of the matrix A.

n 0. When n = 0, ?lanhs is set to zero.

a

REAL for slanhs

DOUBLE PRECISION for dlanhs

COMPLEX for clanhs

DOUBLE COMPLEX for zlanhs

Array, DIMENSION (lda,n). The n-by-n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced.

lda

INTEGER. The leading dimension of the array a.

lda max(n,1).

work

REAL for slanhs and clanhs.

DOUBLE PRECISION for dlange and zlange.

Workspace array, DIMENSION (max(1,lwork)), where lwork n when norm = 'I'; otherwise, work is not referenced.

## Output Parameters

val

REAL for slanhs/clanhs

DOUBLE PRECISION for dlanhs/zlanhs

Value returned by the function.

For more complete information about compiler optimizations, see our Optimization Notice.